Concentration analysis: A quantitative assessment of student states

Multiple-choice tests such as the Force Concept Inventory (FCI) provide useful instruments to probe the distribution of student difficulties on a large scale. However, traditional analysis often relies solely on scores (number of students giving the correct answer). This ignores what can be significant and important information: the distribution of wrong answers given by the class. In this paper we introduce a new method, concentration analysis, to measure how students' responses on multiple-choice questions are distributed. This information can be used to study if the students have common incorrect models or if the question is effective in detecting student models. When combined with information obtained from qualitative research, the method allows us to identify cleanly what FCI results are telling us about student knowledge. (C) 2001 American Association of Physics Teachers.